19 research outputs found
Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence
The problem of 1/f noise has been with us for about a century. Because it is
so often framed in Fourier spectral language, the most famous solutions have
tended to be the stationary long range dependent (LRD) models such as
Mandelbrot's fractional Gaussian noise. In view of the increasing importance to
physics of non-ergodic fractional renewal models, I present preliminary results
of my research into the history of Mandelbrot's very little known work in that
area from 1963-67. I speculate about how the lack of awareness of this work in
the physics and statistics communities may have affected the development of
complexity science, and I discuss the differences between the Hurst effect, 1/f
noise and LRD, concepts which are often treated as equivalent.Comment: 11 pages. Corrected and improved version of a manuscript submitted to
ITISE 2016 meeting in Granada, Spai
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Perspectives on tipping points in integrated models of the natural and human earth system: cascading effects and telecoupling
© Copyright 2022 The Author(s). The Earth system and the human system are intrinsically linked. Anthropogenic greenhouse gas emissions have led to the climate crisis, which is causing unprecedented extreme events and could trigger Earth system tipping elements. Physical and social forces can lead to tipping points and cascading effects via feedbacks and telecoupling, but the current generation of climate-economy models do not generally take account of these interactions and feedbacks. Here, we show the importance of the interplay between human societies and Earth systems in creating tipping points and cascading effects and the way they in turn affect sustainability and security. The lack of modeling of these links can lead to an underestimation of climate and societal risks as well as how societal tipping points can be harnessed to moderate physical impacts. This calls for the systematic development of models for a better integration and understanding of Earth and human systems at different spatial and temporal scales, specifically those that enable decision-making to reduce the likelihood of crossing local or global tipping points.Institute for Basic Science (IBS), Republic of Korea, under IBS-R028-D1; European Union's Horizon 2020 research and innovation programme under grant agreement No. 820712 (REmote Climate Effects and their Impact on European sustainability, Policy and Trade (RECEIPT)); CLICCS Cluster of Excellence (Grant ID: 2037) funded by the German Research Foundation (DFG)
Predicting climate change using response theory: global averages and spatial patterns
The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O(105105) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is non-autonomous as a result of time-dependent forcings. We propose a simple yet efficient method for predicting—at any lead time and in an ensemble sense—the change in climate properties resulting from increase in the concentration of CO22 using test perturbation model runs. We assess strengths and limitations of the response theory in predicting the changes in the globally averaged values of surface temperature and of the yearly total precipitation, as well as in their spatial patterns. The quality of the predictions obtained for the surface temperature fields is rather good, while in the case of precipitation a good skill is observed only for the global average. We also show how it is possible to define accurately concepts like the inertia of the climate system or to predict when climate change is detectable given a scenario of forcing. Our analysis can be extended for dealing with more complex portfolios of forcings and can be adapted to treat, in principle, any climate observable. Our conclusion is that climate change is indeed a problem that can be effectively seen through a statistical mechanical lens, and that there is great potential for optimizing the current coordinated modelling exercises run for the preparation of the subsequent reports of the Intergovernmental Panel for Climate Change
Mechanics and thermodynamics of a new minimal model of the atmosphere
The understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here, we introduce a new model for the atmosphere that is constructed by supplementing the now-classic Lorenz ’96 one-dimensional lattice model with temperature-like variables. The model features an energy cycle that allows for energy to be converted between the kinetic form and the potential form and for introducing a notion of efficiency. The model’s evolution is controlled by two contributions—a quasi-symplectic and a gradient one, which resemble (yet not conforming to) a metriplectic structure. After investigating the linear stability of the symmetric fixed point, we perform a systematic parametric investigation that allows us to define regions in the parameters space where at steady-state stationary, quasi-periodic, and chaotic motions are realised, and study how the terms responsible for defining the energy budget of the system depend on the external forcing injecting energy in the kinetic and in the potential energy reservoirs. Finally, we find preliminary evidence that the model features extensive chaos. We also introduce a more complex version of the model that is able to accommodate for multiscale dynamics and that features an energy cycle that more closely mimics the one of the Earth’s atmosphere
Analysis of a bistable climate toy model with physics-based machine learning methods
We propose a comprehensive framework able to address both the predictability of the first and of the second kind for high-dimensional chaotic models. For this purpose, we analyse the properties of a newly introduced multistable climate toy model constructed by coupling the Lorenz ’96 model with a zero-dimensional energy balance model. First, the attractors of the system are identified with Monte Carlo Basin Bifurcation Analysis. Additionally, we are able to detect the Melancholia state separating the two attractors. Then, Neural Ordinary Differential Equations are applied to predict the future state of the system in both of the identified attractors
Introduction to the special issue on the statistical mechanics of climate
We introduce the special issue on the Statistical Mechanics of Climate by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions